1. Field of the Invention
Embodiments of the present invention relate to high-performance computing. More particularly, embodiments of the present invention relate to systems and methods of computing a solution to a partial differential equation.
2. Description of the Related Art
Many fundamental physical phenomena, such as the behavior of forces, the motion of objects, the thermal energy of a body, the behavior of electric and magnetic fields, the flow of fluids, and the like, are described by partial differential equations (PDEs). The solutions to PDEs are used to solve problems in engineering and scientific endeavors in variety of fields including fluid dynamics, electromagnetic systems, quantum mechanics, meteorology, economics, biochemical systems, and many others. However, in many situations, the computational requirements to solve the PDEs may be prohibitively large and finding the solution may be time consuming. For example, some PDEs may include millions of unknowns and may require thousands of iterations to resolve each unknown. The solution to such a PDE may require days or even weeks utilizing a cluster of computing systems. The large amount of computation time may be unacceptable if the computing systems are needed for other tasks or if the solution is needed sooner. Furthermore, general purpose computers, such as desktop computers and workstations, are equipped to perform a wide variety of tasks that require very little, if any, computational power. Thus, general purpose computers aren't typically equipped with the processing ability to solve PDEs.